Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −0.98. Find the p-value p.

z = −0.98H₁: μ < μ₀

p =

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 36 bottles has a mean of 45.67 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 45.67 mLσ = 10 mLn = 36

z =

3.Medium

A sample of 81 students has a mean score of 500.5 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 500.5s = 4n = 81

t =

4.Medium

Two production lines make the same part. Line 1: a sample of 40 parts has mean length 148 mm, and the line's known standard deviation is 16 mm. Line 2: a sample of 80 parts has mean 144.7 mm, known standard deviation 19 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 40x̄₁ = 148 mmσ₁ = 16 mmn₂ = 80x̄₂ = 144.7 mmσ₂ = 19 mm

z =

5.Hard

A one-sided z test at α = 0.01 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 10. Find the minimum sample size n.

α = 0.01power = 80%δ = 3σ = 10z_α = 2.326z_β = 0.842

n =

6.Hard

A sample of 25 measurements has mean 117.8. The population standard deviation is 5. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 117.8σ = 5n = 2590%

L =

Answer key

1. p = 0.1635
2. z = −2.598
3. t = 1.125
4. z = 0.999
5. n = 112
6. L = 116.2

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